cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A153466 a(n) = A027941(n) + A027941(n+6).

Original entry on oeis.org

232, 610, 1600, 4192, 10978, 28744, 75256, 197026, 515824, 1350448, 3535522, 9256120, 24232840, 63442402, 166094368, 434840704, 1138427746, 2980442536, 7802899864, 20428257058, 53481871312, 140017356880, 366570199330, 959693241112, 2512509524008
Offset: 0

Views

Author

Paul Curtz, Dec 27 2008

Keywords

Links

Programs

  • Mathematica
    LinearRecurrence[{4,-4,1},{232,610,1600},25] (* G. C. Greubel, Aug 19 2016 *)

Formula

a(n) = 3*a(n-1) - a(n-2) + 2.
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3) = 2*A153873(n+3).
G.f.: 2*(116 - 159*x + 44*x^2)/((1-x)*(x^2-3*x+1)).

Extensions

Edited and extended by R. J. Mathar, Sep 09 2009

A153819 Linear recurrence with a(n) = 3a(n-1) - a(n-2) + 2 = 4a(n-1) - 4a(n-2) + a(n-3). Full sequence for A153466.

Original entry on oeis.org

16, 34, 88, 232, 610, 1600, 4192, 10978, 28744, 75256, 197026, 515824, 1350448, 3535522, 9256120, 24232840, 63442402, 166094368, 434840704, 1138427746, 2980442536, 7802899864, 20428257058, 53481871312, 140017356880, 366570199330, 959693241112, 2512509524008
Offset: 0

Views

Author

Paul Curtz, Jan 02 2009

Keywords

Comments

a(n) mod 9 = 7.
A two-way infinite sequence with a(-n) = a(n-1).

Links

Programs

  • Magma
    [18*Fibonacci(2*n+1)-2: n in [0..30]]; // Vincenzo Librandi, Jun 19 2016
  • Mathematica
    LinearRecurrence[{4, -4, 1}, {16, 34, 88} , 100] (* G. C. Greubel, Jun 18 2016 *)
  • PARI
    Vec(2*(8-15*x+8*x^2)/((1-x)*(1-3*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 02 2016

Formula

G.f.: 2*(8-15*x+8*x^2)/((1-x)*(1-3*x+x^2)). - Jaume Oliver Lafont, Aug 30 2009
a(n) = 2*A153873(n) = 18*Fibonacci(2*n+1)-2.
a(n) = (2^(-n)*(-5*2^(1+n)-9*(3-sqrt(5))^n*(-5+sqrt(5))+9*(3+sqrt(5))^n*(5+sqrt(5))))/5. - Colin Barker, Nov 02 2016

Extensions

Edited by Charles R Greathouse IV, Oct 05 2009

A155110 a(n) = 8*Fibonacci(2n+1).

Original entry on oeis.org

8, 16, 40, 104, 272, 712, 1864, 4880, 12776, 33448, 87568, 229256, 600200, 1571344, 4113832, 10770152, 28196624, 73819720, 193262536, 505967888, 1324641128, 3467955496, 9079225360, 23769720584, 62229936392, 162920088592, 426530329384, 1116670899560
Offset: 0

Views

Author

Paul Curtz, Jan 20 2009

Keywords

Links

Crossrefs

Cf. A001519, A027941, A099496, A122367, A153873, A154811, A156551.

Programs

Formula

a(n) = 8*A001519(n+1) = 8*A122367(n) = 8 *|A099496(n)|.
a(n) == A154811(n+6) (mod 9).
a(n) == A156551(n) (mod 10).
a(n) = A153873(n) - A027941(n).
G.f.: 8*(1 - x)/(1 - 3*x + x^2). - G. C. Greubel, Apr 21 2021

Extensions

Comments converted to formulas by R. J. Mathar, Oct 06 2009

A153981 a(n) = 36*Fibonacci(2*n+1) - 4.

Original entry on oeis.org

32, 68, 176, 464, 1220, 3200, 8384, 21956, 57488, 150512, 394052, 1031648, 2700896, 7071044, 18512240, 48465680, 126884804, 332188736, 869681408, 2276855492, 5960885072, 15605799728, 40856514116, 106963742624, 280034713760, 733140398660
Offset: 0

Views

Author

Paul Curtz, Jan 04 2009

Keywords

Links

Programs

  • Magma
    [36*Fibonacci(2*n+1)-4: n in [0..30]]; // Vincenzo Librandi, Aug 07 2011
  • Mathematica
    36*Fibonacci[2*Range[0,30]+1]-4 (* or *) LinearRecurrence[{4,-4,1},{32,68,176},30] (* Harvey P. Dale, Jan 26 2013 *)

Formula

a(n) = 4*A153873(n) = 2*A153819(n).
a(n) = 5 (mod 9) = A010716(n) (mod 9).
a(n) = 3*a(n-1) - a(n-2) + 4.
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3).
a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
G.f.: 4*(8 - 15*x + 8x^2)/((1-x)*(1 -3*x +x^2)). - R. J. Mathar, Jan 23 2009

Extensions

Edited and extended by R. J. Mathar and N. J. A. Sloane, Jan 23 2009
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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